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专业: 理论和计算化学

[求助] 重金求助3道统计作业，200金币求答案，数据附在附件上了

A file on DocDepot in the assignments folder on doc-depot called FamilyIncomes.mtp contains data on the median and average family income in each dissemination area within Ottawa.

a.  Treating the median family incomes as the population, use Minitab to calculate the population mean.  Set aside all population information until part d.
b.  Now use Minitab (Calc Menu – Random Data – Sample from Columns) to draw twenty samples of size n = 31.  This procedure must be replicated twenty times (note that if you open up the same sampling dialog box each time from the menu, then you only have to replace the previous destination column with the next one).  Using each sample, use Minitab to calculate a 95% confidence interval estimate for the population mean, assuming you do not know the population standard deviation (this interval estimation can be done in one operation on all twenty columns).
c.  For the first sample, confirm the Minitab generated interval by calculating the interval manually.  Display the sample data graphically and comment on whether the relevant assumption regarding the population distribution is warranted (state clearly the assumption needed to justify the interval estimation).
d.  Count the number of intervals that contain the true value of the population mean from part a.

2.  In the 2011 federal election, 39.62% of the electorate voted for the Conservative party, 30.63% for the NDP, and 18.91% for the Liberal Party.

(a)  A recent poll of 1000 respondents found 36.3% would support the federal Liberals and 30.4% would support the Conservative Party. Test whether this is sufficient evidence to show that the Conservative vote has dropped by more than 5% from their share of the popular vote in 2011.  Use the .01 level of significance and show your manual calculations.
(b)  Suppose you wanted to estimate the national level of support for the Conservatives using a 99%
2-sided confidence interval with a margin of error of ±1%.  What sample size would be required?
(c)  Suppose that, in a random sample of 17 University of Ottawa students, only 3 indicated a preference for the Conservatives.  Test whether this is sufficient evidence to indicate that the level of support for the Conservatives among U of O students is lower than the 39.62% share of the popular vote in 2011. Use the .05 level of significance and show how you would calculate the p-value for this test.  Why does this not allow us to infer anything about the national level of support for the Conservatives?

3.  A second file on DocDepot named bmi_sample.mtp contains two samples of BMI values from the male and female populations.

a.  Examine the distributions of the sample data to determine if the 2 sample t-test is valid.  Comment.
b.  Test whether there is sufficient evidence to show that the average male BMI is different from the average female BMI in the population.  Use the critical value approach and the .05 level of significance.  Perform the test manually after using Minitab to summarize the data and/or to calculate the degrees of freedom.
c.  Now calculate the p-value for your sample result.
d.  Finally calculate manually the confidence interval for the true difference between the two mean BMIs.
e.  Explain how the results in (c) and (d) are consistent with your conclusion in (b).
f.  If the 2-sample t-test were not valid, then identify another test you could use. Explain.

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